Let Formula: see text be a commutative ring with identity and Formula: see text be an Formula: see text-module. A proper submodule Formula: see text of Formula: see text is said to be prime if for any Formula: see text and Formula: see text with Formula: see text, we have Formula: see text or Formula: see text (Formula: see text). The aim of this paper is to introduce and investigate the notions of lopsided-nil-prime and lopsided-Formula: see text-prime submodules of Formula: see text as two generalizations of prime submodules of Formula: see text.
Faranak Farshadifar (Wed,) studied this question.